Recursive estimation of time-delay using a high-order Pade approximant

The time-delay is a special structure parameter that when unknown greatly complicates the identification problem. To simplify parameter estimation, for use in subsequent system analysis, control and fault detection and diagnosis, it is often useful to have a finite-dimensional approximation of G(s). In this contribution G(s) is approximated using Pade approximants of exp(-sT). Using standard least-squares techniques, a practical drawback is that the number of estimated time-delay parameters increases with the order of the Pade approximation. In this contribution an approach to the recursive estimation of a continuous time-delay system, using discrete measurements, is presented where the number of estimated parameters is independent of the order of the Pade approximation. A partially-known system (PKS) identification technique is used to achieve this.